cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-10 of 18 results. Next

A102145 Iccanobirt prime indices (15 of 15): Indices of prime numbers in A102125.

Original entry on oeis.org

4, 6, 7, 11, 30, 31, 50, 64, 77, 146, 163, 185, 210, 354, 367, 402, 3137, 3228, 3639, 11756, 22054, 23126
Offset: 1

Views

Author

Jonathan Vos Post and Ray Chandler, Dec 31 2004

Keywords

Comments

No more terms through 5000.
a(23) > 50000. - Robert Price, Nov 11 2018

Crossrefs

Cf. A000040, A102125, A102131-A102144.

Programs

  • Mathematica
    a[n_] := a[n] =
   IntegerReverse[IntegerReverse[a[n - 1]] + IntegerReverse[a[n - 2]] +
     IntegerReverse[a[n - 3]]];
a[0] = 0; a[1] = 0; a[2] = 1;
Select[Range[0, 5000], PrimeQ[a[#]] &] (* Robert Price, Apr 10 2020 *)

Formula

A102125(a(n)) = A102165(n).

Extensions

a(20)-a(22) from Robert Price, Nov 11 2018

A102165 Iccanobirt primes (15 of 15): Prime numbers in A102125.

Original entry on oeis.org

2, 7, 31, 941, 7112507, 12796921, 3517479344831, 1899587921740207, 57354010293760755391, 35721164922760679029463000239097478253, 7147924589973841766823293744823574255243111
Offset: 1

Views

Author

Jonathan Vos Post and Ray Chandler, Dec 31 2004

Keywords

Comments

Next term is too large to include.

Crossrefs

Cf. A000040, A102125, A102145, A102151-A102164.

Formula

a(n) = A102125(A102145(n)).

Extensions

Offset changed to 1 by Jinyuan Wang, Aug 14 2021

A102185 Iccanobirt semiprime indices (15 of 15): Indices of semiprime numbers in A102125.

Original entry on oeis.org

5, 15, 16, 19, 20, 21, 22, 24, 28, 29, 35, 38, 44, 54, 58, 59, 72, 84, 106, 108, 137, 145, 174, 227, 238, 253, 258, 362, 363, 371, 388
Offset: 1

Views

Author

Jonathan Vos Post and Ray Chandler, Dec 31 2004

Keywords

Crossrefs

Cf. A001358, A102125, A102171-A102184, A102205.

Formula

A102125(a(n)) = A102205(n).

Extensions

a(24)-a(27) from Robert Price, Nov 11 2018
Offset changed to 1 and a(28)-a(31) from Jinyuan Wang, Aug 15 2021

A102205 Iccanobirt semiprimes (15 of 15): Semiprime numbers in A102125.

Original entry on oeis.org

4, 5071, 6313, 31591, 9853, 11733, 31865, 736481, 9834802, 5123383, 906334841, 312395329, 73044385753, 39216355244851, 353123779923181, 944016528715333, 901870160743125919, 3394064622591216338731, 798539095539570459224764519, 5844680137439021618014007903
Offset: 1

Views

Author

Jonathan Vos Post and Ray Chandler, Dec 31 2004

Keywords

Crossrefs

Cf. A001358, A102125, A102185, A102191-A102204.

Programs

  • Mathematica
    nxt[{a_,b_,c_}]:=With[{ir=IntegerReverse},{b,c,ir[ir[a]+ir[b]+ir[c]]}]; Select[NestList[nxt,{0,0,1},200][[;;,1]],PrimeOmega[#]==2&] (* Harvey P. Dale, Jul 22 2025 *)

Formula

a(n) = A102125(A102185(n)).

Extensions

Offset changed to 1 and a(20) from Jinyuan Wang, Aug 14 2021

A102111 Iccanobirt numbers (1 of 15): a(n) = a(n-1) + a(n-2) + R(a(n-3)), where R is the digit reversal function A004086.

Original entry on oeis.org

0, 0, 1, 1, 2, 4, 7, 13, 24, 44, 99, 185, 328, 612, 1521, 2956, 4693, 8900, 20185, 33049, 53332, 144483, 291848, 459666, 1135955, 2443813, 4246722, 12285846, 19716010, 34278280, 118852511, 154192582, 281332336, 550783729, 1117407516, 2301424427
Offset: 0

Views

Author

Jonathan Vos Post and Ray Chandler, Dec 30 2004

Keywords

Comments

Digit reversal variation of tribonacci numbers A000073.
Inspired by Iccanobif numbers: A001129, A014258-A014260.

Crossrefs

Cf. A102112-A102125, A102131, A102171.

Programs

  • Magma
    a:=[0,0,1];[n le 3 select a[n] else Self(n-1) + Self(n-2) + Seqint(Reverse(Intseq(Self(n-3)))):n in [1..36]]; // Marius A. Burtea, Oct 23 2019
  • Maple
    read("transforms") ;
A102111 := proc(n)
    option remember;
    if n <= 2 then
        return op(n+1,[0,0,1]) ;
    else
        return procname(n-1)+procname(n-2)+digrev(procname(n-3)) ;
    end if;
end proc:
seq(A102111(n),n=0..20) ; # R. J. Mathar, Nov 17 2012
  • Mathematica
    R[n_]:=FromDigits[Reverse[IntegerDigits[n]]];Clear[a];a[0]=0;a[1]=0;a[2]=1;a [n_]:=a[n]=a[n-1]+a[n-2]+R[a[n-3]];Table[a[n], {n, 0, 40}]
nxt[{a_,b_,c_}]:={b,c,IntegerReverse[a]+b+c}; NestList[nxt,{0,0,1},40][[;;,1]] (* Harvey P. Dale, Jul 18 2023 *)
  • Python
    def R(n):
  n_str = str(n)
  reversedn_str = n_str[::-1]
  reversedn = int(reversedn_str)
  return reversedn
def A(n):
  if n == 0:
    return 0
  elif n == 1:
    return 0
  elif n == 2:
    return 1
  elif n >= 3:
    return A(n-1)+A(n-2)+R(A(n-3))
for i in range(0,20):
  print(A(i)) # Dylan Delgado, Oct 23 2019

Formula

A004086(a(n)) = A102119(n).

A102112 Iccanobirt numbers (2 of 15): a(n) = a(n-1) + R(a(n-2)) + a(n-3), where R is the digit reversal function A004086.

Original entry on oeis.org

0, 0, 1, 1, 2, 4, 7, 13, 24, 62, 117, 167, 940, 1818, 2034, 11155, 17275, 74420, 142846, 162568, 885229, 1893336, 2978492, 10197702, 15039830, 38797423, 52888176, 100407789, 206394037, 1246986214, 2077887605, 6411178063, 12726051979
Offset: 0

Views

Author

Jonathan Vos Post and Ray Chandler, Dec 30 2004

Keywords

Comments

Digit reversal variation of tribonacci numbers A000073.
Inspired by Iccanobif numbers: A001129, A014258-A014260.

Links

Crossrefs

Cf. A102111-A102125.

Programs

  • Mathematica
    R[n_]:=FromDigits[Reverse[IntegerDigits[n]]];Clear[a];a[0]=0;a[1]=0;a[2]=1;a [n_]:=a[n]=a[n-1]+R[a[n-2]]+a[n-3];Table[a[n], {n, 0, 40}]
nxt[{a_,b_,c_}]:={b,c,a+FromDigits[Reverse[IntegerDigits[b]]]+c}; Transpose[ NestList[nxt,{0,0,1},40]][[1]] (* Harvey P. Dale, Jul 29 2013 *)

Formula

A004086(a(n)) = A102120(n).

A102124 Iccanobirt numbers (14 of 15): a(n) = R(R(a(n-1)) + R(a(n-2)) + a(n-3)), where R is the digit reversal function A004086.

Original entry on oeis.org

0, 0, 1, 1, 2, 4, 7, 31, 42, 44, 99, 581, 823, 216, 1251, 6592, 3964, 98, 47311, 72451, 99862, 73698, 789881, 684873, 171146, 8359081, 2855313, 6626115, 92901661, 80528542, 25591874, 127303561, 518156392, 14745484, 711014964, 521206301
Offset: 0

Views

Author

Jonathan Vos Post and Ray Chandler, Dec 30 2004

Keywords

Comments

Digit reversal variation of tribonacci numbers A000073.
Inspired by Iccanobif numbers: A001129, A014258-A014260.

Links

Crossrefs

Cf. A102111-A102125.

Programs

  • Maple
    R:= n-> (s-> parse(cat(s[-i]$i=1..length(s))))(""||n):
a:= proc(n) option remember; `if`(n<3, binomial(n, 2),
       R(R(a(n-1)) + R(a(n-2)) + a(n-3)) )
    end:
seq(a(n), n=0..50);  # Alois P. Heinz, Jun 18 2014
  • Mathematica
    R[n_]:=FromDigits[Reverse[IntegerDigits[n]]];Clear[a];a[0]=0;a[1]=0;a[2]=1;a [n_]:=a[n]=R[R[a[n-1]]+R[a[n-2]]+a[n-3]];Table[a[n], {n, 0, 40}]

Formula

a(n) = A004086(A102116(n)).

A102113 Iccanobirt numbers (3 of 15): a(n) = a(n-1) + R(a(n-2)) + R(a(n-3)), where R is the digit reversal function A004086.

Original entry on oeis.org

0, 0, 1, 1, 2, 4, 7, 13, 24, 62, 135, 203, 760, 1593, 1962, 5980, 12622, 16208, 39724, 142606, 265660, 914694, 1587497, 2150478, 10594748, 27283111, 120773124, 216660897, 649176190, 1868619823, 2758358381, 6139199008, 11266906261
Offset: 0

Views

Author

Jonathan Vos Post and Ray Chandler, Dec 30 2004

Keywords

Comments

Digit reversal variation of tribonacci numbers A000073.
Inspired by Iccanobif numbers: A001129, A014258-A014260.

Links

Crossrefs

Cf. A102111-A102125.

Programs

  • Maple
    R:= n-> (s-> parse(cat(s[-i]$i=1..length(s))))(""||n):
a:= proc(n) option remember; `if`(n<3, binomial(n, 2),
       a(n-1) + R(a(n-2)) + R(a(n-3)) )
    end:
seq(a(n), n=0..50);  # Alois P. Heinz, Jun 18 2014
  • Mathematica
    R[n_]:=FromDigits[Reverse[IntegerDigits[n]]];Clear[a];a[0]=0;a[1]=0;a[2]=1;a [n_]:=a[n]=a[n-1]+R[a[n-2]]+R[a[n-3]];Table[a[n], {n, 0, 40}]
nxt[{a1_,a2_,a3_}]:={a2,a3,a3+FromDigits[Reverse[IntegerDigits[ a1]]]+ FromDigits[ Reverse[ IntegerDigits[a2]]]}; Transpose[NestList[nxt,{0,0,1},40]][[1]] (* Harvey P. Dale, Oct 17 2012 *)
nxt[{a_,b_,c_}]:={b,c,c+IntegerReverse[b]+IntegerReverse[a]}; NestList[ nxt,{0,0,1},40][[All,1]] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Sep 10 2016 *)

Formula

A004086(a(n)) = A102121(n).

A102115 Iccanobirt numbers (5 of 15): a(n) = R(a(n-1)) + a(n-2) + R(a(n-3)), where R is the digit reversal function A004086.

Original entry on oeis.org

0, 0, 1, 1, 2, 4, 7, 13, 42, 44, 117, 779, 1138, 9801, 3204, 22135, 57415, 77633, 144214, 541549, 1123036, 7257201, 3095708, 21636315, 55486847, 104580673, 482935860, 247988412, 1073911003, 3317721397, 9220077878, 15106615327, 89503015162
Offset: 0

Views

Author

Jonathan Vos Post and Ray Chandler, Dec 30 2004

Keywords

Comments

Digit reversal variation of tribonacci numbers A000073.
Inspired by Iccanobif numbers: A001129, A014258-A014260.

Links

Crossrefs

Cf. A102111-A102125.

Programs

  • Mathematica
    R[n_]:=FromDigits[Reverse[IntegerDigits[n]]];Clear[a];a[0]=0;a[1]=0;a[2]=1;a [n_]:=a[n]=R[a[n-1]]+a[n-2]+R[a[n-3]];Table[a[n], {n, 0, 40}]
nxt[{a_,b_,c_}]:={b,c,Total[FromDigits/@Reverse/@IntegerDigits[ {a,c}]]+b}; Transpose[NestList[nxt,{0,0,1},35]][[1]] (* Harvey P. Dale, Dec 19 2011 *)

Formula

A004086(a(n)) = A102123(n).

A102116 Iccanobirt numbers (6 of 15): a(n) = R(a(n-1)) + R(a(n-2)) + a(n-3), where R is the digit reversal function A004086.

Original entry on oeis.org

0, 0, 1, 1, 2, 4, 7, 13, 42, 62, 63, 104, 499, 1458, 9639, 18409, 101308, 903221, 943819, 1141966, 8512981, 9527388, 11871383, 55668051, 62931854, 72771964, 148399704, 517843422, 705114520, 398159926, 1173206822, 3621090124, 6895084900
Offset: 0

Views

Author

Jonathan Vos Post and Ray Chandler, Dec 30 2004

Keywords

Comments

Digit reversal variation of tribonacci numbers A000073.
Inspired by Iccanobif numbers: A001129, A014258-A014260.

Links

Crossrefs

Cf. A102111-A102125.

Programs

  • Mathematica
    R[n_]:=FromDigits[Reverse[IntegerDigits[n]]];Clear[a];a[0]=0;a[1]=0;a[2]=1;a [n_]:=a[n]=R[a[n-1]]+R[a[n-2]]+a[n-3];Table[a[n], {n, 0, 40}]
nxt[{a_,b_,c_}]:={b,c,FromDigits[Reverse[IntegerDigits[c]]]+ FromDigits[ Reverse[ IntegerDigits[b]]]+a}; Transpose[NestList[nxt,{0,0,1},40]][[1]] (* Harvey P. Dale, Oct 10 2014 *)

Formula

A004086(a(n)) = A102124(n).
Showing 1-10 of 18 results. Next

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